Provide an appropriate response.Does the graph of f(x) = 
have a tangent at the origin? Give reasons for your answer.
What will be an ideal response?
The function f is not differentiable at x = 0 and hence does not have a tangent at the origin.
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Solve the problem.A weight attached to a spring is pulled down 4 inches below the equilibrium position. Assuming that the frequency of the system is 
cycles per second, determine a trigonometric model that gives the position of the weight at time t seconds.
A. s(t) = 4? cos 5t
B. s(t) = 4 cos 10t
C. s(t) = -4 cos 
t
D. s(t) = -4 cos 10t
Solve the problem.Ken is 6 feet tall and is walking away from a streetlight. The streetlight has its light bulb 14 feet above the ground, and Ken is walking at the rate of 1.6 feet per second. Find a function, d(t), which gives the distance Ken is from the streetlight in terms of time. Find a function, 
, which gives the length of Ken's shadow in terms of d. Then find 
.
A. (S ? d)(t) = 0.88t B. (S ? d)(t) = 1.52t C. (S ? d)(t) = 1.2t D. (S ? d)(t) = 2.7t
Choose the graph that models the situation best.The cost of buying x calculators at a price of $110 each
A. 
B. 
C. 
D. 
Solve the following quadratic equation by factoring.
a. 
b. 
c. 
d. 
e. 